Statistical tests are often performed to make decisions about whether the groups in an experiment are similar or different. The most basic example is to compare the outcomes of an experimental group and a control group. Inferential statistics provide an objective method for interpreting experiment outcomes.
When two groups are equal or very similar, the difference is called not significant. This means that the two groups are close enough to be treated as being essentially the same. In contrast, big differences between groups that seem to be nonrandom differences are called statistically significant differences.
The classic approach to inferential testing works by calculating a test score, such as z (from standard scores), t (from t-tests), or F (from analysis of variance). The score is then used to determine a probability from a probability distribution, which is informally called a p value. A p > .05 is usually judged as nonsignificant, whereas a p < .05 is judged as being statistically significant.
The following information covers traditional or classical approaches to inferential statistics that a beginning statistician might use. These approaches are sometimes called null hypothesis testing or frequentist statistics.
There is increasing awareness that the interpretation of classic inferential statistics can be problematic. Null hypothesis testing approaches have come under increasing criticism in recent years. New approaches, such as Bayesian-based statistics, are gaining in popularity. However, these newer inferential statistics are beyond the current goal of helping the beginning statistician get started.
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